# Thread: Square of an exponential function: simpler form?

1. ## Square of an exponential function: simpler form?

It's part of a quantum course, but the problem I'm having is pretty straight math.

There are two similar functions I need to square. I can do it fine, but the question calls for 'simplified form' and I'm struggling to simplify.

They are $\displaystyle 1-e^{-iat}$ and $\displaystyle 1+e^{-iat}$. Take the subtraction example (the only difference with the other one is a sign): I get $\displaystyle 1-2e^{-iat}+e^{-2iat}$.

Is there a way to express this more simply?

2. ## Re: Square of an exponential function: simpler form?

Use [TEX] ... [/TEX] tags instead of $$...$$ tags.

Edit: Looks like you already did.

3. ## Re: Square of an exponential function: simpler form?

Originally Posted by Bravus
Is there a way to express this more simply?
Not really. You can factor out $\displaystyle e^{-iat}$ from the last two terms, but this is not much simpler.

4. ## Re: Square of an exponential function: simpler form?

Thanks very much. Guess I'll check with the tutor tomorrow and see whether they had something in mind, but it's reassuring that at least I wasn't just missing something simple. ;-)

Thanks again.

5. ## Re: Square of an exponential function: simpler form?

AAaahh. Just to wrap up the question in case anyone else has a similar one.

My mistake was that in quantum mechanics 'squaring' is actually (sometimes) shorthand for multiplying something by its complex conjugate, rather than simply by itself. I needed to multiply $\displaystyle (1-e^{-iat})$ by $\displaystyle (1-e^{iat})$... and *that* does get simpler, particularly with some judicious application of Euler's identity.

Thanks again.

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